Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization

PDDL2.1: An extension of PDDL for expressing temporal planning domains

In recent years research in the planning community has moved increasingly towards application of planners to realistic problems involving both time and many types of resources. For example, interest in planning demonstrated by the space research community has inspired work in observation scheduling, planetary rover ex ploration and spacecraft control domains. Other temporal and resource-intensive domains including logistics planning, plant control and manufacturing have also helped to focus the community on the modelling and reasoning issues that must be confronted to make planning technology meet the challenges of application. The International Planning Competitions have acted as an important motivating force behind the progress that has been made in planning since 1998. The third competition (held in 2002) set the planning community the challenge of handling time and numeric resources. This necessitated the development of a modelling language capable of expressing temporal and numeric properties of planning domains. In this paper we describe the language, PDDL2.1, that was used in the competition. We describe the syntax of the language, its formal semantics and the validation of concurrent plans. We observe that PDDL2.1 has considerable modelling power --- exceeding the capabilities of current planning technology --- and presents a number of important challenges to the research community

Processes and continuous change in a SAT-based planner

AbstractThe TM-LPSAT planner can construct plans in domains containing atomic actions and durative actions; events and processes; discrete, real-valued, and interval-valued fluents; reusable resources, both numeric and interval-valued; and continuous linear change to quantities. It works in three stages. In the first stage, a representation of the domain and problem in an extended version of PDDL+ is compiled into a system of Boolean combinations of propositional atoms and linear constraints over numeric variables. In the second stage, a SAT-based arithmetic constraint solver, such as LPSAT or MathSAT, is used to find a solution to the system of constraints. In the third stage, a correct plan is extracted from this solution. We discuss the structure of the planner and show how planning with time and metric quantities is compiled into a system of constraints. The proofs of soundness and completeness over a substantial subset of our extended version of PDDL+ are presented

Planning as Quantified Boolean Formulae

This work explores the idea of classical Planning as Quantified Boolean Formulae. Planning as Satisfiability (SAT) is a popular approach to Planning and has been explored in detail producing many compact and efficient encodings, Planning-specific solver implementations and innovative new constraints. However, Planning as Quantified Boolean Formulae (QBF) has been relegated to conformant Planning approaches, with the exception of one encoding that has not yet been investigated in detail. QBF is a promising setting for Planning given that the problems have the same complexity. This work introduces two approaches for translating bounded propositional reachability problems into QBF. Both exploit the expressivity of the binarytree structure of the QBF problem to produce encodings that are as small as logarithmic in the size of the instance and thus exponentially smaller than the corresponding SAT encoding with the same bound. The first approach builds on the iterative squaring formulation of Rintanen; the intuition behind the idea is to recursively fold the plan around the midpoint, reducing the number of time-steps that need to be described from n to log₂n. The second approach exploits domain-level lifting to achieve significant improvements in efficiency. Experimentation was performed to compare our formulation of the first approach with the previous formulation, and to compare both approaches with comparative and state-of-the-art SAT approaches. Results presented in this work show that our formulation of the first approach is an improvement over the previous, and that both approaches produce encodings that are indeed much smaller than corresponding SAT encodings, in both terms of encoding size and memory used during solving. Evidence is also provided to show that the first approach is feasible, if not yet competitive with the state-of-the-art, and that the second approach produces superior encodings to the SAT encodings when the domain is suited to domain-level lifting.This work explores the idea of classical Planning as Quantified Boolean Formulae. Planning as Satisfiability (SAT) is a popular approach to Planning and has been explored in detail producing many compact and efficient encodings, Planning-specific solver implementations and innovative new constraints. However, Planning as Quantified Boolean Formulae (QBF) has been relegated to conformant Planning approaches, with the exception of one encoding that has not yet been investigated in detail. QBF is a promising setting for Planning given that the problems have the same complexity. This work introduces two approaches for translating bounded propositional reachability problems into QBF. Both exploit the expressivity of the binarytree structure of the QBF problem to produce encodings that are as small as logarithmic in the size of the instance and thus exponentially smaller than the corresponding SAT encoding with the same bound. The first approach builds on the iterative squaring formulation of Rintanen; the intuition behind the idea is to recursively fold the plan around the midpoint, reducing the number of time-steps that need to be described from n to log₂n. The second approach exploits domain-level lifting to achieve significant improvements in efficiency. Experimentation was performed to compare our formulation of the first approach with the previous formulation, and to compare both approaches with comparative and state-of-the-art SAT approaches. Results presented in this work show that our formulation of the first approach is an improvement over the previous, and that both approaches produce encodings that are indeed much smaller than corresponding SAT encodings, in both terms of encoding size and memory used during solving. Evidence is also provided to show that the first approach is feasible, if not yet competitive with the state-of-the-art, and that the second approach produces superior encodings to the SAT encodings when the domain is suited to domain-level lifting

Efficient Automated Planning with New Formulations

Problem solving usually strongly relies on how the problem is formulated. This fact also applies to automated planning, a key field in artificial intelligence research. Classical planning used to be dominated by STRIPS formulation, a simple model based on propositional logic. In the recently introduced SAS+ formulation, the multi-valued variables naturally depict certain invariants that are missed in STRIPS, make SAS+ have many favorable features. Because of its rich structural information SAS+ begins to attract lots of research interest. Existing works, however, are mostly limited to one single thing: to improve heuristic functions. This is in sharp contrast with the abundance of planning models and techniques in the field. On the other hand, although heuristic is a key part for search, its effectiveness is limited. Recent investigations have shown that even if we have almost perfect heuristics, the number of states to visit is still exponential. Therefore, there is a barrier between the nice features of SAS+ and its applications in planning algorithms. In this dissertation, we have recasted two major planning paradigms: state space search and planning as Satisfiability: SAT), with three major contributions. First, we have utilized SAS+ for a new hierarchical state space search model by taking advantage of the decomposable structure within SAS+. This algorithm can greatly reduce the time complexity for planning. Second, planning as Satisfiability is a major planning approach, but it is traditionally based on STRIPS. We have developed a new SAS+ based SAT encoding scheme: SASE) for planning. The state space modeled by SASE shows a decomposable structure with certain components independent to others, showing promising structure that STRIPS based encoding does not have. Third, the expressiveness of planning is important for real world scenarios, thus we have also extended the planning as SAT to temporally expressive planning and planning with action costs, two advanced features beyond classical planning. The resulting planner is competitive to state-of-the-art planners, in terms of both quality and performance. Overall, our work strongly suggests a shifting trend of planning from STRIPS to SAS+, and shows the power of formulating planning problems as Satisfiability. Given the important roles of both classical planning and temporal planning, our work will inspire new developments in other advanced planning problem domains

The GRT Planning System: Backward Heuristic Construction in Forward State-Space Planning

This paper presents GRT, a domain-independent heuristic planning system for STRIPS worlds. GRT solves problems in two phases. In the pre-processing phase, it estimates the distance between each fact and the goals of the problem, in a backward direction. Then, in the search phase, these estimates are used in order to further estimate the distance between each intermediate state and the goals, guiding so the search process in a forward direction and on a best-first basis. The paper presents the benefits from the adoption of opposite directions between the preprocessing and the search phases, discusses some difficulties that arise in the pre-processing phase and introduces techniques to cope with them. Moreover, it presents several methods of improving the efficiency of the heuristic, by enriching the representation and by reducing the size of the problem. Finally, a method of overcoming local optimal states, based on domain axioms, is proposed. According to it, difficult problems are decomposed into easier sub-problems that have to be solved sequentially. The performance results from various domains, including those of the recent planning competitions, show that GRT is among the fastest planners

Planning Graph as a (Dynamic) CSP: Exploiting EBL, DDB and other CSP Search Techniques in Graphplan

This paper reviews the connections between Graphplan's planning-graph and the dynamic constraint satisfaction problem and motivates the need for adapting CSP search techniques to the Graphplan algorithm. It then describes how explanation based learning, dependency directed backtracking, dynamic variable ordering, forward checking, sticky values and random-restart search strategies can be adapted to Graphplan. Empirical results are provided to demonstrate that these augmentations improve Graphplan's performance significantly (up to 1000x speedups) on several benchmark problems. Special attention is paid to the explanation-based learning and dependency directed backtracking techniques as they are empirically found to be most useful in improving the performance of Graphplan

TALplanner in IPC-2002: Extensions and Control Rules

TALplanner is a forward-chaining planner that relies on domain knowledge in the shape of temporal logic formulas in order to prune irrelevant parts of the search space. TALplanner recently participated in the third International Planning Competition, which had a clear emphasis on increasing the complexity of the problem domains being used as benchmark tests and the expressivity required to represent these domains in a planning system. Like many other planners, TALplanner had support for some but not all aspects of this increase in expressivity, and a number of changes to the planner were required. After a short introduction to TALplanner, this article describes some of the changes that were made before and during the competition. We also describe the process of introducing suitable domain knowledge for several of the competition domains